quadrants

Quadrants are a way of dividing a space into four equal parts by two perpendicular lines that meet at a common point. In plane geometry, this most often refers to the Cartesian quadrants created by the x- and y-axes. Points on the axes themselves do not belong to any quadrant. The four standard regions are Quadrant I (x > 0, y > 0), Quadrant II (x < 0, y > 0), Quadrant III (x < 0, y < 0), and Quadrant IV (x > 0, y < 0). The concept extends to higher dimensions, though the labeling differs (e.g., octants in three dimensions). The name reflects the quarter-circle origin of the term.

In mathematics and science, quadrants help describe the sign combination of coordinates, vectors, or variables. In the complex plane, the real and imaginary axes divide the plane into four quadrants. Quadrant analysis is also used in data visualization and statistics, where points in a scatter plot are categorized into Q1 through Q4 to summarize patterns.

In anatomy, the abdomen is often described in four quadrants by two perpendicular planes intersecting at the navel: the right upper quadrant and left upper quadrant, and the right lower quadrant and left lower quadrant. This division assists clinical assessment and diagnosis, though alternative nine-region methods exist for more detail.

Historically, a quadrant is also an instrument dating from antiquity and the medieval period used to measure the altitude of celestial bodies or the angle of elevation. The term comes from the Latin quadrans, meaning a quarter of a circle.